Free Throw shooting is an important aspect of the game; it is essential that all athletes no matter their position are successful from the Free Throw line. With Coaching, most athletes will approach the free throw line by first aligning their feet. If right handed, the right foot would align with the split line, slightly in front of the left foot, shoulder width apart.  This will ensure that the athlete is stable and balanced when shooting the ball. The reason that the right foot aligns with the spilt line is so that the ball should only miss long or short therefore making it more accurate and there is less to adjust in your shot after you miss. Each athlete is different but most takes one or two dribbles of the basketball and then brings the ball up onto their fingers where the index finger aligns with a groove on the ball, and then the athlete will shoot the ball. Holding their follow through by locking their elbow and snapping their wrist. This YouTube clip gives a good and accurate explanation of how to shoot a Free Throw. 

http://www.youtube.com/watch?v=-N2a8epAW_0

Source: This picture was taken from  http://www.lunch.com/reviews/sports_league/UserReview-NBA-1453236-158114-Underhanded_Free_Throws_Time_For_a_Comeback_.html   This picture illustrates the teaching cues of a Free Throw. 

The Answer: 

Newton’s Laws:

First Law: 'An object will remain at rest or continue to move with constant velocity as long as the net force equals zero' (Blazevich, 2010, p.44). The tendency of an object to remain in its present state is called Inertia. All objects with a mass have inertia, the larger the mass the more inertia to overcome therefore making it more difficult to speed up, slows down or change direction (Blazevich, 2010, p. 44). When shooting a Free Throw the athlete needs to change their state from rest to a vertical motion.

Second Law: ‘The acceleration of an object is proportional to the net force acting on it and inversely proportional to the mass of the object F=M x A’ (Blazevich, 2010, p. 45) in order to change a state of motion it is required to apply force. The equation F= M×A tells us that to accelerate an object faster we must apply more force (Blazevich, 2010, p. 45). To shoot a Free Throw, the athlete must apply force in order to accelerate the ball.

Third Law: ‘For every action, there is an equal and opposite reaction’ (Blazevich, 2010, p. 45).  When we walk, run or jump we apply force against earth, the earth applies an equal and opposite force in order to move us. This is evident in the Free Throw when a vertical or downward force is applied when the foot contacts the ground, the ground exerts an equal and opposite reaction force. These forces can accelerate the athlete forward or vertical if the force is great enough to overcome inertia. 

Source: Blazevich, 2010, p.45. This diagram demonstrates how we must apply a downward force in order for an equal and opposite reaction to propel us into the air vertically.

The Law of Gravitation: ‘All bodies are attracted to each other with a force proportional to the product of the two masses and inversely proportional to the square of the distance between them’ (Blazevich, 2010, p. 46).

Gravity will have less influence if the product of two masses is smaller; therefore Gravitational force is less when we are lighter. The net force causing acceleration in the upward direction is equal to the upward directional force plus the downwards gravitational force (this is a negative factor as it acts downwards). Inertia is relative to the mass of the object, so heavier objects require a larger force to accelerate, this is enlarged when an object is moving vertically because of the gravitational force. Which is evident in a Free Throw as the athlete is moving vertically, bending their legs and applying force into the ground, to come up on to their toes or to jump slightly. So, because of gravitational force we much use a larger force.

All three of Newton’s Laws and the Law of Gravitation work together to allow the athlete to come up onto their toes or jump slightly to shoot the Free Throw. The athlete needs to overcome inertia by having a applied force against them, to do this they must apply a large and well-directed force against the earth which applies an equal and opposite reaction force against them, which also the shooter to come up into their toes or jump slightly. Because of Newton’s law of gravitation it is necessary to produce large vertical forces, or have a low body mass in order to jump higher. 

Source: (Taken by H. Richards) This picture shows how the athlete bends their knees in order to apply force to accelerate the object.

Projectile Motion:

This is the motion of an object projected at an angle into the air. Factors that can influence an objects trajectory include gravity and air resistance.  A projection can move at any angle between 0 degrees (horizontal) or 90 degrees (vertical). Trajectory is influenced by the projection speed, the projection angle and the relative height of projection (Blazevich, 2010, p. 25).

Projection speed: the distance and projectile covers is determined by its projection speed, the faster the speed the further it will go. In the free throw the projectile or the basketball moves vertically, therefore the projection speed will determine the height is reaches before gravity accelerates it back to earth.

Projectile angle: This affects the range of a projectile. When an object is projected at angles between 0 degrees and 90 degrees, the object will travel vertically and horizontally. When the angle is greater the object attains greater vertical height but less range.

Relative height of projection: This is the vertical distance between the projection point of an object and the point in which it lands.

This greater angle is good for a Free Throw the optimum angle for a Free Throw is approximately 51 degrees (Gordon, 1997, p. 495).  As this needs a greater angle of projection to improve the accuracy of the shot, the ball is more likely to go in if it falls vertically then when it skims across the top of the basket. In the end it would be necessary to run biomechanical tests to determine the optimum trajectory for the basketball, based on the individual athlete who is shooting it because of physiological features such as height or arm length can alter the optimum angle. 

Source: Photo taken from  http://en.zero.wikipedia.org/wiki/Lauren_Jackson: 
 This demonstrates how the athlete releases the ball from a large angle to allow the ball to fall vertically into the ring.

The Magnus Effect:

This YouTube clip gives a good general understanding of the Magnus effect:

http://www.youtube.com/watch?v=23f1jvGUWJs

By understanding the importance of Spin, performance of the Free Throw can be improved.  By Appling more backspin on the basketball if you shot long or short you have a higher change of the ball going in if it has backspin because it is more likely to bounce up and drop into the basket (Hubbard, 206, pp. 1303-1308). Soft hands on the ball is crucial, this is done by the athlete having the ball on their fingers and no part of the ball touching on the palm of their hands. By the action of snapping the wrist it allows the ball to come off the fingers with backspin.

Momentum:

We need force to get an object to exert velocity in order to overcome inertia. If the force is exerted in the correct direction we will be accelerated in the desired direction. In order to change an objects momentum we need to apply force. To accelerate vertically we need larger vertical impulses, this will propel us into the air. Impulse is a production of force and time therefore the greater the impulse the greater the change in momentum (Blazevich, 2010, pp. 52-54). This biomechanical principle is present in a foul shot when the athlete is bending their legs pushes force as a vertical impulse into the ground in order to propel themselves up onto their toes or in to propel themselves into the air slightly.

Summation of Forces:  

The sum of forces is the momentum given to the object in this case the ball generated by each body part. To generate maximum momentum using each segment of the body from the large muscles in the legs into the small muscles last to generate force.  Correct timing, through to the great range of motion will gain maximum momentum (Brancazio, 1981, p. 358). To attain power, efficacy and accuracy in the shot the whole body is used. The shot begins with the movement of the legs, pushing into the ground. The force then travels from the legs into the shoulders, into the forearms and into the tips of the fingers when the ball is released. 

Source: Picture Taken from  http://offthebackboard.wordpress.com/2011/07/17/the-list-best-free-throw-routines/   This picture illustrates how the muscles work together in summation to generate force.

Kinetic Chain:

A Push like movement pattern is when we move as if we are pushing something. This is when we extend all joints simultaneously in a single movement. Because everything is acting together the cumulative forces generated about each joint result in a high overall force (Blazevich, 2010, p. 196). Push like movements are very efficient. As the joint rotations are simultaneous this results in a straight-line movement of the end point of the chain, this movement therefore has accurate results. We see this push like movement pattern in a Free Throw when the athlete extends their knee and elbow joints simultaneously in order to generate force to push the ball in a straight-line movement. 

Source: This picture was taken from  http://zjcist195.blogspot.com.au  The photo demonstrates how the knee and elbow joints extend, producing force in order to push the ball forwards and vertically. 

Work, Energy and Power

‘The amount of work done is equal to the average force that is applied multiplied by the distance of which it is applied. W= F x D’ (Blazevich, 2010, p. 100).

This is a product of force and displacement, force provided over a range of object movement.

Power is the ‘rate of doing work, work per unit time or the product of force and velocity’ (Blazevich, 2010, pp. 101-102).

Kinetic energy is associated with velocity of our body or a motion of a body with greater mass (Blazevich, 2010, p. 103). Kinetic energy is present in a Free Throw as there is movement of the athlete’s body.

By understanding the relationship between work, power and energy we can improve performance of a Free Throw. All these components of power, work and energy are present when the athlete is bending up and onto their toes in order to push the ball up towards the basket; it is present throughout the whole action of the Free Throw.

How else we can use this information:

The Netball shot and a set shot in basketball are very closely related to the biomechanical principles of a Free Throw. In an Netball shot athletes with align their feet with the basket and then bend their knees, pushing into the ground in order to propel their feet into the air, just like a Free Throw the only difference between these two shots is the follow through where basketball athletes lock and snap their wrist of the shooting hand and netballers follow through with two hands. A set shot in basketball is where an athlete is open for a shot with no defenders on them (just like a Foul Shot), so all that is required for the athlete is to catch and shoot. The only difference in the two shots is the force required for the athlete to propel himself or herself into the air higher.

The biomechanical principles like newton’s second law, vertical impulse, work, power and the kinetic chain can all be altered in order to maximise other aspects of the sport of basketball such as the component of rebounding where the principle can be used to maximise jump height and energy required for repeated jumps. This may also relate to volleyball where blockers have to not only jump high but also lower their energy cost for repeated jumps. Another component of basketball where some principles relate are the dunk where athletes need to jump high and stretch up with a angle to get the ball over the ring.

References:

Blazevich, A. (2010). Sports biomechanics, the basics: Optimising human performance. A&C Black.

Brancazio, P. J. (1981). Physics of basketball. American Journal of Physics, 49, 356-365.

Gordon R, Hamilton & Christoph, Reinschmidt. (1997). Optimal Trajectory for the basketball free throw. Journal of Sports Sciences, 15(5), 491-504.

Hubbard, H & Okubo, M. (2006). Dynamics of the basketball shot with application to the free throw. Journal of sports science, 24(12), 1303.